Path-Loss Model for Broadcasting Applications and Outdoor Communication Systems in the VHF and UHF Bands

Transcription

1 IEEE TRANSACTIONS ON BROADCASTING, VOL. 48, NO. 2, JUNE Path-Loss Model for Broadcasting Applications and Outdoor Communication Systems in the VHF and UHF Bands Constantino Pérez-Vega, Member, IEEE, and José M. Zamanillo Abstract A simple propagation model for the VHF and UHF bands is presented. The model is a computational form of the data provided by the FCC F(50,50) propagation curves, and it is aimed to be used by practicing engineers. It allows the estimation of median path loss, received power, or electrical field strength which usually is sufficient in many practical applications. The model is independent of frequency and is applicable to outdoor environments in a range of distances from about 0.5 mi (800 m) up to 40 mi (64.36 km) and transmitting antenna heights from 100 ft (30.48 m) up to 2000 ft (609.6 m), and is based on a receiving antenna height of 30 ft (9 m). Index Terms Outdoor propagation, path loss, propagation models. I. THEORETICAL BASIS THE MODEL studied here is intended for use in coverage prediction of broadcasting services in the VHF and UHF bands. Since the model is not frequency-dependent [6], it can also be used in other types of communication systems in these bands. The model is of easy application and does not require particular computational resources. Actually, the model is no other thing than a mathematical characterization of the FCC F(50,50) propagation curves [1] and allows the estimation of the median value of path loss as a function of frequency, distance and transmitting antenna height. In the model, path loss is characterized by an attenuation factor, in this case, the exponent of distance; i.e., it is assumed that received power does not follow an inverse square law of distance as in free space propagation, but a law of the inverse of distance raised to an exponent [2] [5], [9], [10], in general greater than 2, even when in particular environments, such as aisles in buildings or tunnels, it can take values smaller than 2 [11]. In this paper, the model is intended for outdoor propagation where the values of the exponent are, in general, greater than 2. In this model, the received isotropic power at a distance d from the transmitter is given by watt (1) where is the effective isotropic radiated power in the direction of the receiver, is the distance between transmitting and receiving antennas in meters, and is the wavelength in me- Manuscript received October 16, 2001; revised May 9, The authors are with the Communications Engineering Department, University of Cantabria, Santander, Spain ( constantino.perezv@unican.es). Publisher Item Identifier S (02) ters. The value of intrinsically embeds the effects of all propagation mechanisms: attenuation, diffraction, reflection, etc. No attempt is made to establish a relationship between and the physical aspects of the channel. However, it seems clear that the higher the effects of scattering mechanisms, such as attenuation, diffraction, diffuse reflections, etc., the smaller the received power, and the higher the value of. Path loss in db is usually expressed as, therefore, from (1), it can be calculated as db (2) where is in meters. If, in (2), is given in miles, path loss can be calculated as where is the attenuation at 1 m in free space: db (3) Model (2) has been used for indoor as well as outdoor communications, and several versions have been treated previously in [2] [5], [9] [11]. It also must be stated that no simple relationship can be established between and the various and, in general, complex physical processes that affect path loss. In general, it is not possible to quantify the individual effects of the scatterers and, therefore, the predictions that can be obtained with any propagation model, including this one, are only an approximation. In any case, the reasonably accurate estimation of path loss is fundamental in the power budget of any communication system. In the aforementioned expressions, no clear dependence of with frequency, distance or antenna height appears. In order to establish the dependence of with respect to frequency, a campaign of measurements was performed at various frequencies in the VHF and UHF bands, from 100 MHz to 800 MHz, and the results are reported in [6]. It appears that is independent of frequency, a result that is in concordance with the findings reported in [6] and with the very nature of the F(50,50) propagation curves. On the other hand, the dependence of respect to distance and transmitting antenna height is not evident, and a vast amount of measurements would be required in order to establish such dependence experimentally. Instead of that, we attempted an indirect approach using the data obtained from the FCC F(50,50) propagation curves for television broadcasting in the VHF and (4) /02$ IEEE

2 92 IEEE TRANSACTIONS ON BROADCASTING, VOL. 48, NO. 2, JUNE 2002 Fig. 1. Exponent of distance versus antenna height in feet for constant distance in miles. UHF bands. An empirical model was developed, that is applicable to outdoor propagation environments at distances between around 0.5 and 40 miles (0.8 to 64 km). It must be noted that does also depend on receive antenna height. The model presented here is based on a fixed receive antenna height of 30 ft (9 m) which, in general, is sufficient for practical purposes, and a correction procedure for other receive antenna heights is given in Section IV. It is well known that the FCC F(50,50) propagation curves have been in use successfully since many years by practicing engineers, and provide adequate estimations of field strength, and indirectly, of received power for a vast amount of practical cases. Such curves were developed using measured values, taken in different geographical areas over different periods of time, and provide the median values of field strength for service at 50% of locations during 50% of the time. Therefore, such curves reflect reliable experimental data not derived from theoretical models [7]. It must be stated, however, that the model proposed here does not pretend to be better than others in use. It is a well-known fact that different propagation models often yield conflicting results and it depends on the experience and good judgment of the engineer the final decision on what particular model reflects better the practical results. The model presented here offers an alternative of easy application by practicing engineers which are always faced with the frequently difficult choice between predictions or calculations, and measurements [8] and, in some way, combines both in a simple way. Furthermore, the model is independent of the type of communication system; i.e., if it is analog or digital, but it does not provide any information about angles of arrival, delay spread, etc., neither it provides any other information about channel dynamics; only the mean (or median) value of path loss, which is sufficient for most practical applications. II. DEPENDENCE OF THE MODEL WITH DISTANCE AND TRANSMITTING ANTENNA HEIGHT To establish the dependence of with distance and transmitting antenna height, field strength values were obtained from a set of F(50,50) curves, for distances from 1 to 40 miles (1.6 to km), and for transmitting antenna heights from 100 up to 2000 ft. The curves assume a constant receiving antenna height of 30 ft (9 m) and corrections must be made for other heights [8]. For distances up to about 30 miles (48.3 km) the F(50,50) curves for frequencies above 470 MHz are not based on measured data, and theory would indicate that the field strength should decrease more rapidly with distance beyond the horizon for frequencies in the VHF band [1]. Several sets of field strength values were taken for constant height at different distances, and analyzed afterwards. In this analysis British units were used, so appropriate care must be taken if SI units are used, since the coefficients of the model are not the same in the two systems of units. In the Appendix, the adequate coefficients in SI units are also presented. Even when field strength values from the curves are referred to an EIRP [ in (1)] of 1 kw, calculation of the isotropic received power is straightforward for any other vale of and the value of can be easily obtained from (1) as (dbw) (dbw) where is defined by (4) and the equivalent isotropic radiated power ( ), as well as the isotropic received power ( ) are in the same logarithmic units (dbw or dbm). The latter can be easily obtained from the field strength as (5) watt (6)

3 PÉREZ-VEGA AND ZAMANILLO: PATH-LOSS MODEL FOR BROADCASTING APPLICATIONS 93 Fig. 2. Exponent of distance versus distance in miles for constant antenna height in feet. where is the field strength in V/m obtained from the F(50,50) curves, and it must be stressed that in the above equations, is the median value of the exponent of distance. Actually, the mean and median values of the exponent differ only in the order of 1% and, for our purposes, are considered as equivalent here. The procedure followed to obtain the value of from the F(50,50) curves was, first, to read in the curves the values of for different transmitting antenna heights and distances, then using (6), obtain and, finally, obtain using (5). From (5) it seems apparent that depends on distance; however, the relation is not straightforward since also varies with distance. If the dimensions of the coverage area are small, such as those found in indoor or cellular environments of small radius, the mean value of is fairly constant [2] and no clear dependence of with appears. To establish such dependence, either measurements in a considerable range of distances are required, or alternatively, as done in this paper, use already existing data such as provided by the F(50,50) curves. As can be appreciated from Figs. 1 and 2, the exponent of distance is a function of two variables, distance and transmitting antenna height. It is also a function of the receiving antenna height, however, for our purposes here, a constant receiving antenna height of 30 ft (9 m) was assumed, since the F(50,50) curves are based on this assumption. Actually, three models can be derived from Figs. 1 and 2. One in which varies with distance and the transmitting antenna height is kept constant, which is the usual practical case. Other in which varies with antenna height keeping the distance constant. The previous two models are unidimensional, and a more complete bidimensional model where can also be derived and is the one we present in this paper. TABLE I COEFFICIENTS OF THE MODEL III. THE MODEL Following the procedure described in the previous section, a set of values of for different distances and transmitting antenna heights was obtained, and several attempts to fit the values of to mathematical functions were made, namely: logarithmic, exponential, and polynomial. The best fit was obtained with a polynomial model of fourth degree with the form Fitting was performed with Stanford Graphics software to obtain the coefficients when is in feet and in miles. Such coefficients are given in Table I, and in the Appendix, the corresponding coefficients for SI units, i.e., for in meters and in km. It must be noted that even when some of the coefficients appear to be very small and, apparently, they could be neglected, for example, if is made zero, the results deviate considerably from the correct ones as or increase. Therefore, all coefficients with the decimal places shown, must be used in implementing the model. Simpler, unidimensional models with less coefficients can also be derived for as a function of distance or (7)

4 94 IEEE TRANSACTIONS ON BROADCASTING, VOL. 48, NO. 2, JUNE 2002 Fig. 3. Field strength versus antenna height in feet for constant distance in miles. transmitting antenna height alone. The model presented here is the more general bidimensional model, applicable to both cases. that would be expected at 30 ft, and the field at a receiver antenna height is [8] IV. PROCEDURE TO OBTAIN THE RECEIVED POWER AND THE ELECTRIC FIELD STRENGTH FROM THE MODEL Model (7) provides the value of the exponent of distance in terms of transmitting antenna height and distance between transmitter and receiver. In order to obtain the received power, or the electric field strength, several calculations are required, as shown here. a) The value of being known using (7), path loss in db is calculated using (2) or (3). b) Isotropic receiver power is now calculated in logarithmic units as (dbw) (8) where is the equivalent isotropic radiated power (EIRP) in the direction of the receiver, and is the path loss in db. c) Finally, the field strength can be calculated from (6) as V/m (9) As stated in Section I, model (7) is based on a receive antenna height of 30 ft (9 m), therefore, the received fields must be corrected for other heights. There is not a definite procedure to specify the adequate correction factor, however, the usual practice is to assume that field strength increases linearly with receiver antenna height, as indicated by classical propagation theory. With this assumption, the relationship between the field (10) where is the field strength at 30 ft and is the field at a receive antenna height. The above procedure can be easily implemented in any computer, or even pocket calculators, and allows the calculation of field strength or received power with practically the same precision as the F(50,50) curves. However, it must be stressed that any rounding of the coefficients given here will produce large errors and render the model unreliable. As stated in Section I, the very nature of the F(50,50) curves and, therefore, of the model, is not frequency dependent in the band of interest here, so it can be used to estimate the path-loss not only for television broadcasting, but also for other radioelectric communication systems such as radiotelephony and mobile communications. The model is intended to be used by practicing engineers and provides an estimation of the median value of path-loss, which is sufficient in many practical applications where a deeper knowledge of channel dynamics is not necessary. It does not provide information on issues such as fade margins, angles of arrival, or delay spread, which must be estimated by other means. V. RESULTS The model fits very well with the values read from the F(50,50) curves as can be appreciated from Figs In Figs. 1 and 2, the variation of the exponent of distance is plotted with respect to antenna height and distance, respectively. Figs. 3

5 PÉREZ-VEGA AND ZAMANILLO: PATH-LOSS MODEL FOR BROADCASTING APPLICATIONS 95 Fig. 4. Field strength versus distance in miles for constant antenna height in feet. Fig. 5. Exponent of distance as a function of transmitting antenna height and distance in SI units. and 4 show the field strength for both cases. In the figures, broken lines with circles indicate values from FCC curves and continuous lines, the values calculated with the model The maximum deviation between the values of obtained from the curves, and those calculated with the model is of 1.23%. The maximum deviation between the field strengths obtained from the curves and with the model is of 0.48 db, with maximum errors of about 0.65 db. VI. CONCLUSION A simple computational path loss model has been derived from the FCC F(50,50) curves. Such curves were developed using measured values, taken in different geographical areas over different periods of time, and provide the median values of field strength for service at 50% of locations during 50% of the time. Therefore, such curves reflect reliable experimental data not derived from theoretical models. In the model, the exponent

6 96 IEEE TRANSACTIONS ON BROADCASTING, VOL. 48, NO. 2, JUNE 2002 of distance is characterized as a function of distance and transmitting antenna height. From this parameter, mean, or median path loss, receiving power, and field strength are easily obtained. Fitting of the model with F(50,50) curves is very good for distances between 0.5 mi and 40 mi and antenna heights up to 2000 ft. Values are based on a receiving antenna height of 30 ft, therefore, corrections are necessary for other heights. The model does not require particular computational effort and is of simple application for practicing engineers who do not require a deeper knowledge of channel dynamics. The model is also independent of frequency and may be used for broadcasting applications as well as for other radioelectric communication systems in the VHF and UHF bands where the F(50,50) curves are applicable. APPENDIX MODEL COEFFICIENTS FOR SI UNITS When transmitting antenna height is given in meters, and distance in kilometers, the following coefficients must be used in model (7). Also, a 3-D plot of the exponent of distance with respect to distance and transmitting antenna height in SI units, is shown in Fig. 5. REFERENCES [1] Federal Communications Commission, Code of Federal Regulations,, Title 47. Ch. 1, Part 73, Radio Broadcast Services. Secs , and [2] C. Perez-Vega and J. L. Garcia, A simple approach to a statistical path-loss model for indoor communications, in 27th Europ. Microwave Conf. Proc., Jerusalem, [3] D. C. Cox et al., 800-MHz attenuation measured in and around suburban houses, BTSJ, vol. 63, no. 6, pp , Aug [4] J. B. Andersen, T. Rappaport, and S Yoshida, Propagation measurements and models for wireless communication channels, IEEE Commun. Mag., pp , Jan [5] C. Perez-Vega and J. M. Zamanillo, Indoor propagation at 2.45 GHz for TV applications, in Proc. Microwave Symp (MS 2000), Tetuan, Morocco, May [6] C. Perez-Vega and J. L. Garcia, Frequency behavior of a power-law path loss model, in Proc. 10th Microcoll., Budapest, March [7] M. H. Barringer and K. D. Springer, Radio wave propagation, in NAB Eng. Handbook, 8th ed. Washington, DC: NAB, 1992, ch [8] J. W. Stielper, The measurement of FM and TV field strengths (54 MHz 806 MHz), in NAB Eng. Handbook, 8th ed. Washington, DC: NAB, 1992, ch [9] T. S. Rappaport, Wireless Communications: Principles and Practice: IEEE Press - Prentice-Hall PTR, [10] A. J. Motley and J. M. P. Keenan, Personal communication radio coverage in buildings at 900 MHz and 1700 MHz, Electron. Lett., vol. 204, no. 12, pp , [11] S. E. Alexander, Characterising buildings for propagation at 1900 MHz, Electron. Lett., vol. 19, no. 20, p. 860, Sept. 28, Constantino Pérez-Vega was born in Asturias, Spain, in He is an Electronics and Communications Engineer from the Escuela Superior de Ingeniería Mecánica y Eléctrica of México (1965) and received the Ph.D. degree in telecommunications engineering from the University of Cantabria in Santander, Spain (1997). He held several technical managing positions in the Mexican Government Radio and Television System since 1972, and was Director of Engineering at the Instituto Mexicano de Televisión, as well as Technical Advisor at the Dirección General de Radio, Televisión y Cinematografia of the Secretaría de Gobernación in México up to He has been also dedicated to teaching since 1966 in México, and from 1989 until the present, he has been a Professor with the University of Cantabria in the areas of television and communication systems. José M. Zamanillo was born in Madrid, Spain, in He received the B.Sc. and Ph.D. degrees in physics from the University of Cantabria, Spain, in 1988 and 1996, respectively. Since 1988, he has been devoted to education and research at the University of Cantabria where he is Associate Professor. He has been engaged in various European and Spanish projects, mainly in the fields of microwaves and device modeling. Presently, his research interests include linear and nonlinear modeling of GaAs MESFETs, HEMTs, (HBTs), and microwave active devices.